Discrete Component
Audio-Frequency RC Filters
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Web Page Introduction
Building audio filters for home built popcorn receivers using
discrete components for the active elements can be both fun and instructive.
What components go into a given filter is often determined by which parts are on
hand at the time of construction. Presented is a loose collection of filter
ideas and whenever possible, the design theory. Practical examples are included
which were tested in a basic direct conversion receiver using a diode ring mixer
with various AF preamplifiers and an LM386N power amplifier driving headphones.
Basic Resistance-Capacitance Filter Design
Presented in Figure 1 are some basic examples of simple
resistance-capacitance filters. Low frequencies are attenuated by a series
capacitor and a shunt resistor to ground. Conversely, high frequencies are
attenuated by a series resistor with a shunt capacitor to ground. The formula
for the 3 dB cutoff frequency which is the frequency in which the reactance of
the capacitor equals the resistance component value is shown below along with
two derivations.
The normal response of these networks is a 6dB drop in
output voltage per octave. A faster drop can be achieved by cascading filters in
series as is shown in Figure 1 with the series lowpass filter using 2 networks.
Unfortunately, interactions between the two series filter sections will change
the cutoff frequency from the design frequency somewhat. Lowpass, highpass,
bandpass and band-reject (notch) filters can be made using RC networks although
this web page will focus mainly on the lowpass and bandpass
types.
Although, many amateurs are now using LC network designs or
low-noise operational amps for receiver audio filters, RC filters using discrete
components can be low cost and practical alternatives. RC networks enjoy some
advantage over LC networks, namely they do not pickup inductive hum and they are
frequently less expensive and more compact in size.
Interstage Filters
Discussion
Early transistorized AF amplifier stages were mostly
transformer coupled from stage to stage. Eventually, RC-coupling became popular
and with the advent of the silicon transistor direct coupling 2 or greater
stages became common practice. Direct coupling increases low frequency response
and often reduces the parts counts used in AF preamp circuits. RC and direct
coupling allows the designer to shape the stage frequency response using
resistor and capacitors in numerous different network configurations. This
section will focus on interstage filtering RC-coupled amplifiers.
Every amplifier has an optimal frequency range that it
will operate over. RC-coupled stages maybe designed to operate over a frequency
range that best suits the radio amateur. In Figure 2a , we see can see that the
coupling capacitor CC is really in series with the two resistors RC and RL. At
midrange to high audio frequencies, the reactance of CC is negligible and there
will be very little AC voltage drop over it. If we lower the audio frequency,
the capacitive reactance CC will increase by the formula XC = 1 / 6.283 x
Frequency x CC. The lower the frequency, the greater the voltage drop across
capacitor CC will be. If the frequency is lowered to the point where the the
capacitive reactance of CC is equal to the the series resistance of the circuit
the AC voltage drop will be 3dB down from the source voltage.
Figure 2b shows
the voltage source equivalent of figure 2a. In these diagrams, it is important
to note that the value of RL represents the total input impedance of the
subsequent transistor stage. For a given RC and RL, the greater the CC value,
the greater the low frequency response. This fact is often conversely used by
radio amateurs to attenuate 60 cycle hum by using high value capacitors such as
0.1uF for coupling caps.
Emitter bypass caps also can have an effect on the
low frequency response of an amplifier. The lower the XC of an emitter bypass
cap, the greater the low frequency response. A rule of thumb is to use a bypass
capacitor with an XC of 100 or less at the lowest frequency you wish to amplify.
Project
Shown in Figure 3a and 3b are two RC-coupled PNP amplifier
stages that form an interstage bandpass filter using shunt and series
capacitors. If the 3dB lowpass cutoff frequency is at least ten times the 3dB
highpass cutoff filter, the two filters can be considered independent of one
another.
The basic design formulas are shown however they do require some
clarification.
The 3dB highpass cutoff frequency is the frequency where the
reactance of of the coupling capacitor CC equals the series resistance of the
input impedance of Q2 plus resistor RL of Q1. While the RL value is straight
forward, the input impedance is a more complex affair. Figure 2a shows how Q2
looks in terms of its AC input resistance. The input resistance is composed of
R1, R2 and the Q2 emitter resistor. In order to calculate the AC emitter
resistance, the DC emitter Current (Ie) must be first calculated using a
calculator or computer program. Get a transistor textbook if you do not know how
to do this or just assume 1 mA for Ie. To calculate the AC emitter resistance
r'e in ohms, divide Ie into 26.
The formulas are shown in Figure 3a. The base
resistance is calculated by multiplying the transistor Beta by the sum of r'e
plus RE which is the resistance value of the component resistors hooked to the
Q2 emitter. If the emitter is bypassed, make RE zero, if emitter degeneration is
used, the resistance value RE will be the resistance of the unbypassed resistor.
To solve for the AC input resistance, use the parallel circuit formula for R1,
R2 and R input.
The 3dB lowpass cutoff frequency is is the frequency in
which the reactance of the shunt capacitor CS is equal to the resistance of RL
in parallel with the input resistance of Q2 (R input calculated as
above).
Figure 3b shows a practical interstage filter with a low and highpass
cutoff near the desired 10 times differential. Of interest, is the emitter
degeneration on Q2. This is done to raise the AC input resistance of Q2,
stabalize the amp, reduce distortion and to aid in setting the filter capacitor
values. The calculated values are shown to the right of the figure 3b schematic.
A PSPICE run of the 3b interstage filter can be found on this AF Filter Supplemental
Page
The Flicker Receiver
Below in Figure 4 is a minimal parts direct conversion receiver
that I built using the above interstage filter concept. This project was
inspired by Wes Hayward's MicroMountaineer project from QST for 1973 and Solid
State Design. It is both a great challenge and thrill to build and operate
minimalistic rigs. All that is required for this receiver is a front-end
bandpass filter. The double-tuned filter portrayed in the 30M Receiver Project
was used in my version. The diode ring mixer was a TUF-1 by Mini-Circuits as it
is smaller than the SBL-1. The capacitor value used for CS was 0.1uF which sets
the 3dB lowpass cutoff frequency at around 638 Hz. This might seem low, but
since there is only one lowpass filtering network, I prefer to go low and start
rolling the highs off as quickly as possible. If you do not have the 0.22uF CC
capacitor, you can use a two 0.1 uF caps in parallel which gives a calculated
3dB highpass cutoff of ~80 Hertz. Obviously the 10 times low-to-high pass filter
seperation rule was somewhat ignored in this receiver design, but it seems to
work alright. In addition, do not expect dramatic lowpass filtering from just
one RC network. It is interesting that the CS capacitor substantially reduced
broadcast interference problems in the receiver when it was first tested
ungrounded and then after soldered to ground.
The 3 stage preamplifiers have
considerable gain and drive the final and headphones with good volume. At full
volume, AF feedback may erupt if leads and connecting wires are excessively
long. Although my version does not have hum problems, one possible improvement
would be to add the active decoupler to the first stage. It is found in every
other receiver on this web site and would minimize any chance of 60 Hertz hum
getting into the Q1 stage. This little receiver does a good job for so few parts
and can be built extremely compactly.
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A video capture of the prototype Flicker circuit board laying
on the Flicker schematic is shown immediately below. Note that room on the
ground plane was left for further experimentation. The object to the right is
the LM386N upside down with pins 2 and 4 soldered to the copper circuit
board.
Below the prototype board is an actual receiver with an antenna
lowpass filter installed in a Hammond 4 X 3 inch die-cast case as part of a
personal version of W7ZOI's MicroMountaineer transceiver. The loose red and
black wires are temporary B+ and antenna cables used in testing the receiver.
The crystal oscillator, sidetone and transmitter stages have not yet been
installed. The transmitter puts out 1 watt onto the 30 Meter band and features
solid state T/R switching. This is one of my all time favorite projects and has
provided many hours of fun and even some DX.
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It is important to note that the formulas given for interstage
RC filter data are simplistic and do not account for other factors such as
parasitic, Miller effect and wiring capacitance and the frequency to gain
dependence of the active device. The results however will be ballpark and
provide a practical approach for your designs.
I have built a few successful
active filters using nJFETs in both common drain and as source followers. With
these transistors, the low frequency calculations are similar to those of BJTs.
To use the Figure 3a formula for the highpass 3dB cutoff frequency, R input
would be the gate resistance and RL the source resistance of the previous stage.
For the high frequency calculations, things get more complex and the effects of
the circuit and component capacitance come into play. The lowpass formula maybe
used but the CS value will be a bit low in most cases. The actual 3dB cutoff
value maybe somewhat different than the design value. Experimentation will lead
you to good fun and enhanced knowledge of electronics.
Fourth Order Peaked Lowpass Audio Filter
Peaked Lowpass Filter
Shown in Figure 4, is an excellent lowpass filter designed by
Wes Hayward, W7ZOI and was presented in the now defunct HAM RADIO magazine for
April 1974. For the original article, Wes built a ten pole filter however, a
four pole version is shown in Figure 4. I built a filter having eight poles and
was very impressed with its performance during testing on 40 meters with crowded
band conditions. At the input is a single pole section used to properly bias the
succeeding stages and to provide a high pass response, attenuating low
frequencies and 60 - 120 Hertz hum. Following the input stage are pairs of NPN
and PNP transistors which form a 2 pole filter pair that make a unity gain,
non-inverting amp with very high input impedance due to the wrap-around
feedback. The feedback from the collector of the PNP transistor back to the
emitter of the NPN transistor takes the very high gain of the two stages and
forces it back to a voltage gain of 1.
The Q of each filter pair is 1.9
giving a 6dB bandwidth of 200 Hertz. The center frequency is 540 Hertz and
attenuation of the ten pole filter is 75dB at 1200 Hertz. The net gain of the
ten pole filter is 28 dB. Transistor choices include 2N3904 or lower noise
equivalents for the NPN transistors and 2N3906 or lower noise equivalents for
the PNP BJTs. example: 2N3565, 2N5089, 2N5087, 2N3638 etc. Allowable component
tolerances are 10 - 20 % with minimal degradation of performance.
A PSPICE
run of the 4 pole filter shown can be found on this AF Filter Supplemental
Page
Solid State Design for the Radio Amateur contains additional
useful information on building discrete component audio filters. For fun, I
connected the 4 pole filter to a modified Flicker receiver prototype and was
suitably impressed.
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Miscellaneous Filters
Single
common emitter audio filter/amplifier stages maybe used in popcorn receivers.
Below is a collection of four such amplifiers. Figure A has a 300 hertz
bandwidth with a center frequency of 800 hertz. Voltage gain is 1. Figure B has
a low pass response with a breakaway frequency of 3 KHz. Figure C has a bandpass
response center frequency of 1 KHz and is Figures B and D cascaded. Figure D has
a highpass response with a cutoff frequency of 360 Hz. Figure B, B and D have a
no load voltage gain of ~20. All filters can be built using the ubiquitous
2N3904 or equivalent NPN BJT. The cutoff frequencies maybe changed up tp three
decades by changing the capacitor values by a common factor. Trial and error or
SPICE simulation are practical approaches as no design equations are available.
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A Electronics Workbench simulation of the 6A amp can be found
on the AF Filter
Supplemental Page
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